Contextual collaborative filtering via hierarchical matrix factorization

Abstract

Matrix factorization (MF) has been demonstrated to be one of the most competitive techniques for collaborative filtering. However, state-of-the-art MFs do not consider contextual information, where ratings can be generated under different environments. For example, users select items under various situations, such as happy mood vs. sad, mobile vs. stationary, movies vs. book, etc. Under different contexts, the preference of users are inherently different. The problem is that MF methods uniformly decompose the rating matrix, and thus they are unable to factorize for different contexts. To amend this problem and improve recommendation accuracy, we introduce a "hierarchical" factorization model by considering the local context when performing matrix factorization. The intuition is that: As ratings are being generated from heterogeneous environments, certain user and item pairs tend to be more similar to each other than others, and hence they ought to receive more collaborative information from each other. To take the contextual information into consideration, the proposed "contextual collaborative filtering" approach splits the rating matrix hierarchically by grouping similar users and items together, and factorizes each sub-matrix locally under different contexts. By building an ensemble model, the approach further avoids over-fitting with less parameter tuning. We analyze and demonstrate that the proposed method is a model-averaging gradient boosting model, and its error rate can be bounded. Experimental results show that it outperforms three state-of-the-art algorithms on a number of real-world datasets (Movie- Lens, Netflix, etc). The source code and datasets are available for download1. Copyright © 2012 by the Society for Industrial and Applied Mathematics.